17.1.1.2. Truncation Error

Try these first

1. 1.

   Define local truncation error.

   Hint

   Remember the single step context.

2. 2.

   What does GTE stand for?

   Hint

   Think about how errors accumulate.

3. 3.

   What is the formula for Local Truncation Error in Euler’s method?

   Hint

   Recollect the basic formula applied in Euler's method.

4. 4.

   True or False: Global truncation error is accumulated from local truncation errors.

   Hint

   Think about how each step's error contributes to the total.

5. 5.

   Using Euler's method, calculate the local and global truncation errors for $h = 0.1$ over the interval [0, 1] for the differential equation $dy/dx = y$ with $y(0)=1$.

   Hint

   Look for patterns in how errors accumulate across the defined interval.

6. 6.

   Explain the trade-off between accuracy and computational resources when choosing step sizes in truncation errors.

   Hint

   Think about both sides of the accuracy versus computational cost argument.